Two kinds of contact problems in three-dimensional icosahedral quasicrystals

Two kinds of contact problems, i.e., the frictional contact problem and the adhesive contact problem, in three-dimensional （3D） icosahedral quasicrystals are dis- cussed by a complex variable function method. For the frictional contact problem, the contact stress exhibits power singularities at the edge of the contact zone. For the adhe- sive contact problem, the contact stress exhibits oscillatory singularities at the edge of the contact zone. The numerical examples show that for the two kinds of contact problems, the contact stress exhibits singularities, and reaches the maximum value at the edge of the contact zone. The phonon-phason coupling constant has a significant effect on the contact stress intensity, while has little impact on the contact stress distribution regu- lation. The results are consistent with those of the classical elastic materials when the phonon-phason coupling constant is 0. For the adhesive contact problem, the indentation force has positive correlation with the contact displacement, but the phonon-phason cou- pling constant impact is barely perceptible. The validity of the conclusions is verified.

Elastic analysis of a mode Ⅱ crack in an icosahedral quasicrystal

Based on the displacement potential functions, the elastic analysis of a mode Ⅱ crack in an icosahedral quasicrystal is performed by using the Fourier transform and dual integral equation theory. By the solution, the analytic expressions for the displacement field and stress field are obtained. The asymptotic behaviours of the phonon and phason stress fields around the crack tip indicate that the stresses near the crack tip exhibit a square root singularity. The most important physical quantities of fracture theory, crack stress intensity factor and energy release rate, are evaluated in an explicit version.

MICROSTRUCTURE FORMATION AND MECHANICAL PROPERTY INVOLVING ICOSAHEDRAL QUASICRYSTAL PHASE OF Y RICH Mg-Zn-Y QUASICRYSTAL ALLOY

The microstructure formation and mechanical property involving icosahedral quasicrystal （I-phase） in the Y-rich Mg-Zn-Y alloy have been studied. The equilibrium formation of I-phase from the Y-rich Mg-Zn-Y melt is through a peritectic reaction between the Y-rich melt and the primary W-phase, which is discussed in detail. The independent nucleation and coupling growth mechanism between the W-phase and the I-phase, from the melt, are revealed, which is significant for understanding the peritectic reaction process involving icosahedral quasicrystal in the Mg-Zn-Y alloy. The mechanism of the quasicrystal phase strengthened magnesium alloys is also discussed here.

Icosahedral quasicrystals solids with an elliptic hole under uniform heat flow

The complex variable method for solving the two-dimensional thermal stress problem of icosahedral quasicrystals is stated. The closed-form solutions for icosahedral quasicrystals containing an elliptical hole subjected to a remote uniform heat flow are obtained. When the hole degenerates into a crack, the explicit solutions for the stress intensity factors is presented.

Generalized 2D problem of icosahedral quasicrystals containing an elliptic hole

The generalized 2D problem of icosahedral quasicrystals containing an elliptic hole is considered by using the ex- tended Stroh formalism. The closed-form solutions for the displacements and stresses are obtained under general loading conditions. The solution of the Griffith crack problem as a special case of the results is also observed. The stress intensity factor and strain energy release rate are given. The effect of the phonon-phason coupling elastic constant on the mechanical behavior is also discussed.

Study on a straight dislocation in an icosahedral quasicrystal with piezoelectric effects

An electro-elastic analysis is performed on an icosahedral quasicrystal with piezoelectric effects containing a straight dislocation. The closed-form expressions for the elastic and electric fields are obtained using the extended Stroh formalism. The effects of piezoelectric constant on the phonon displacement, phason displacement, and electric potential are discussed in detail.

Investigation on the icosahedral quasicrystal phase in Mg_(70.8)Zn_(28)Nd_(1.2) alloy

Mg70.8Zn28Nd1.2（mole fraction） alloy containing icosahedral quasicrystal phase （I-phase） was prepared under conventional metal casting conditions. The microstructure, phase constitution and phase structure of the alloy were investigated by means of scanning electron microscopy （SEM）, X-ray diffraction （XRD）, energy dispersive spectrometer （EDS） and transmission electron microscopy （TEM）. The resuits showed that the spherical phase in Mg70.8Zn28Nd1.2 alloy was a simple icosahedral quasicrystal with stoichiometric composition of Mg40Zn55Nd5 and quasi-lattice of 0.525 nm. In this research, the as-cast microstructure of Mg70.8Zn28Nd1.2 alloy mainly consisted of Mg40Zn55Nd5 icosahedral quasicrystal phase and Mg7Zn3 columnar crystal matrix. In the growing process of Mg40Zn55Nd5 icosahedral quasicrystal phase, the growth morphology mainly depended on interface energy, adsorption effect of Nd and cooling rate.

Icosahedral quasicrystal structure of the Mg_(40)Zn_(55)Nd_(5) phase and its thermodynamic stability

The quasicrystal phase is beneficial to increasing the strength of magnesium alloys.However,its complicated structure and unclear phase relations impede the design of alloys with good mechanical properties.In this paper,the Mg_(40)Zn_(55)Nd_(5) icosahedral quasicrystal(I-phase)structure is discovered in an as-cast Mg-58Zn-4Nd alloy by atomic resolution high-angle annular dark-field scanning transmission electron microscopy(HAADF-STEM).A cloud-like morphology is observed with Mg_(41.6)Zn_(55.0)Nd_(3.4) composition.The selected area electronic diffrac-tion(SAED)analysis shows that the icosahedral quasicrystal structure has 5-fold,4-fold,3-fold,and 2-fold symmetry zone axes.The thermo-dynamic stability of the icosahedral quasicrystal is investigated by differential scanning calorimetry(DSC)in the annealed alloys.When an-nealed above 300℃,the Mg_(40)Zn_(55)Nd_(5) quasicrystal is found to decompose into a stable ternary phase Mg_(35)Zn_(60)Nd_(5),a binary phase MgZn,andα-Mg,suggesting that the quasicrystal is a metastable phase in the Mg-Zn-Nd system.

Processing HREM Image of Mn-Al Icosahedral Quasicrystal

THE high resolution electron microscopic (HREM) images of Al-Mn icosahedral quasicrystals (QC) with the incident beam along the five-fold symmetry axis

Dynamic behaviour of the icosahedral Al-Pd-Mn quasicrystal with a Griffith crack

The dynamic response of an icosahedral Al-Pd Mn quasicrystal with a Griffith crack to impact loading is investigated in this paper. The elastohydrodynamic model for the wave propagation and diffusion together with their interaction is adopted. Numerical results of stress, displacement and dynamic stress intensity factors are obtained by using the finite difference method. The effects of wave propagation, diffusion and phonon-phason coupling on the quasicrystal in the dynamic process are discussed in detail, where the phason dynamics is explored particularly.

Finite size specimens with cracks of icosahedral Al Pd Mn quasicrystals

Icosahedral quasicrystals are the most important and thermodynamically stable in all about 200 kinds of quasicrystals currently observed. Beyond the scope of classical elasticity, apart from a phonon displacement field, there is a phason displacement field in the elasticity of the quasicrystal, which induces an important effect on the mechanical properties of the material and makes an analytical solution difficult to obtain. In this paper, a finite element algorithm for the static elasticity of icosahedral quasicrystals is developed by transforming the elastic boundary value problem of the icosahedral quasicrystals into an equivalent variational problem. Analytical and numerical solutions for an icosahedral A1-Pd-Mn quasicrystal cuboid subjected to a uniaxial tension with different phonon-phason coupling parameters are given to verify the validity of the numerical approach. A comparison between the analytical and numerical solutions of the specimen demonstrates the accuracy and efficiency of the present algorithm. Finally, in order to reveal the fracture behavior of the icosahedral A1-Pd-Mn quasicrystal, a cracked specimen with a finite size of matter is investigated, both with and without phonon-phason coupling. Meanwhile, the geometry factors are calculated, including the stress intensity factor and the crack opening displacement for the finite-size specimen. Computational results reveal the importance of pbonon-phason coupling effect on the icosahedral A1-Pd-Mn quasicrystal. Furthermore, the finite element procedure can be used to solve more complicated boundary value problems.

3D Morphology and Formation Process of the Icosahedral Quasicrystalline Phase in Rapidly Solidified Al-Mn Alloy

Three-dimensional morphology and formation process of icosahedral quasicrystal phase have been investigated in a melt-spun AI-18Mn alloy （in wt%）. Three distinct layers corresponding to varying temperature gradient have been observed on the cross section of the ribbons. 3D morphologies of cellular and dendritic icosahedral phase have been obtained through electro-etching. A model has been proposed to describe the formation process of the icosahedral phase and a-A1 during the rapid solidification. The icosahedral phases are primarily precipitated from the melt into fine cellular and dendritic particles, and subsequently engulfed by the a-A1 which propagates in a planar morphology.

Regenerating deuterium absorption of Ti_(36)Zr_(40)Ni_(20)Pd_4 icosahedral quasicrystal

Ti/Zr-based icosahedral quasicrystals are a kind of promising hydrogen storage ma- terials, however their absorption regeneration after oxidation-poisoning has been scarcely studied. This work is intended to investigate the deuterium-storage re- generation of a suction-cast Ti36Zr40Ni20Pd4 quasicrystal. It was found that only through hot vacuuming the quasicrystal could be refreshed from air-flow poisoning to absorb deuterium in two cycles. During the first absorption course, a pregnancy period was observed before the real deuterium uptake while deuterium was loaded rapidly during the second one. The deuterium concentration in the alloy can reach 0.011 mol.D2/（g.M） （corresponding to a hydrogen mass percent of 2.2%. D2 and M denote molecular deuterium and the metallic alloy）. But the loaded deuterium was very difficult to release completely even by eight-stage desorption at different tem- peratures. After the second desorption, the quasicrystal phase remained in a small volume, as though the desorption temperature was beyond the crystallization temperature of the quasicrystal. This probably is attributed to the solution function of residual deuterium in the alloy.

Growth morphology and evolution of quasicrystal in as-solidified Y-rich Mg-Zn-Y ternary alloys

A petal-like icosahedral quasicrystal with five branches,which is considered to be the representative morphology of the icosahedral quasicrystal,has been observed in the Y-rich Mg-Zn-Y ternary alloys. Moreover,the polygon-like morphology,another pattern of the icosahedral quasicrystal,has also been found in the Y-rich Mg-Zn-Y ternary alloys. The latter morphology results from the evolution of the former one. The growth mechanism of the petal-like morphology of the icosahedral quasicrystal was also discussed. Alloying composition,i.e.,Y element content,is a major factor inducing the morphology evolution of the icosahedral quasicrystal.

Microstructures and Morphology Evolution of Icosahedral Phase of As-cast Mg_(67.4)Zn_(28.9)Y_(3.7) Ternary Alloy Subjected to the Pouring Temperature

The microstructure, chemical composition and morphology evolution of icosahedral quasicrystalline phase of Mg67.4Zn28.9Y3.7 ternary alloy were investigated in detail at different pouring temperatures by X-ray diffraction （XRD）, scanning electron microscopy （SEM） and energy-dispersive spectrum （EDS）. Low interracial energy favors the formation of l-phase. The experimental results show that the primary l-phase reveals petal-shaped with five and six branches, where each branch has facetted growth morphology with the size ranging from 50 to 100μm. As the temperature decreases, the polygon-shaped l-phase forms, attributed to the decomposition of branch of petal-shaped l-phase, and then it grows bigger and some of the fine polygons join together to form large polygons. Besides these, （α-Mg＋l-phase） eutectic structures disappear and the relative amount of Mg7Zn3 phase increases as the pouring temperature decreases. The chemical composition and morphology evolution of l-phase were also discussed.

Interface of quasicrystal and crystal

A model on the coexisting phase of quasicrystal-crystal is proposed, with which we concretely investigate the inter- face effects for coexisting phases of one-dimensional orthorhombic quasicrystal-isotropic crystal and three-dimensional icosahedral quasierystal-cubic crystal. The phason strain fields which play an important role in some processes are determined. Some factors affecting the strain fields, e.g., the material constants of phonon, phason, phonon-phason coupling of the quasicrystal and the elastic modulus and the size of the crystal are also explored.

MICROSTRUCTURES AND PROPERTIES OF RECIPROCATINGLY EXTRUDED Mg-6.4Zn-1.1Y ALLOYS

An icosahedral Mg3 YZn6 quasicrystalline phase can be produced in Mg-Zn- Y system alloys when a proper amount of Zn and Y is contained, and it is feasible to prepare the quasicrystal phase-reinforced low-density magnesium alloy. In this article, phase constituents and the effect of reciprocating extrusion on microstructures and properties of the as-cast Mg-6.4Zn-1.1 Y alloy are analyzed. The microstructure of the as-cast Mg-6.4Zn-1.1 Y alloy consists of the α-Mg solid solution, icosahedral Mg3YZn6 quasicrystal, and Mg3 Y2Zn3 and MgZn2 compounds. After the alloy was reciprocatingly extruded for four passes, grains were refined, Mg3 Y2 Zn3 and MgZn2 phases dissolved into the matrix, whereas, Mg3 YZn6 precipitated and distributed uniformly. The alloy possesses the best performance at this state; the tensile strength, yield strength, and elongation are 323.4 MPa, 258.2 MPa, and 19.7%, respectively. In comparison with that of the as-cast alloy, the tensile strength, yield strength, and elongation of the reciprocatingly extruded alloy increase by 258.3%, 397.5%, and 18 times, respectively. It is concluded that reciprocating extrusion can substantially improve the properties of the as-cast Mg-6.4Zn-1.1 Y alloy, particularly for elongation. The high performance of the Mg-6.4Zn-1.1 Y alloy after reciprocating extrusion can be attributed to dispersion strengthening and grain-refined microstructures.

Crystallographic and electrochemical characteristics of melt-spun Ti-Zr-Ni-Cu alloys

Ti44Zr32Ni22Cu2 and Ti41Zr29Ni28Cu2 alloys were prepared by the melt-spinning method. The phase structure was analyzed by X-ray diffraction,and the electrochemical performances of the melt-spun alloys were investigated. The results indicated that the Ti44Zr32Ni22Cu2 alloy was composed of the icosahedral quasicrystals and amorphous phases,and the Ti41Zr29Ni28Cu2 alloy comprised icosahedral quasicrystals,amorphous,and Laves phases. The maximum discharge capacity was 141 mAh/g for the Ti44Zr32Ni22Cu2 alloy and 181 mAh/g for the Ti41Zr29Ni28Cu2 alloy,respectively. The Ti41Zr29Ni28Cu2 alloy also showed a better high-rate dischargeability and cycling stability. The better electrochemical properties should be ascribed to the high content of Ni,which was beneficial to the electrochemical kinetic properties and made the alloy more resistant to oxidation,as well as to the Laves phase in the Ti41Zr29Ni28Cu2 alloy,which could work as the electro-catalyst and the micro-current collector.

Effect of La on the crystalline and electrochemical properties of Ti-Zr-Ni melt-spun alloys

Ti45Zr30Ni25 and Ti45Zr30Ni25La alloys were prepared by melt-spinning, and the phase structure and electrochemical performances of the melt-spun alloys were investigated. The results showed that the Ti45Zr30Ni25 alloy was composed of the quasicrystalline phase, amorphous phase and Laves phase. The Ti45Zr30Ni25La alloy contained quasicrystalline and amorphous phases. The maximum discharge capacity was 111 mAh/g for the Ti45Zr30Ni25 alloy electrode, and 124 mAh/g for the Ti45Zr30Ni25La alloy electrode. The Ti45Zr30Ni25La alloy electrode exhibited a better high-rate dischargeability and cycling stability than the Ti45Zr30Ni25 alloy electrode. The improvement of electrochemical properties was mainly ascribed to the increase in the amorphous phase due to the addition of La.

Amorphous in a Zr-IQC-DQC pseudo-ternary alloy system

A pseudo-ternary alloy system was constructed by combining an icosahedralquasicrystal (IQC), a decagonal quasicrystal (DQC), and Zr into one alloy system. Differentproportions of Zr were added to pseudo-binary alloy IQC_(80)DQC_(20) (mass fraction in %);Structural evolution in these alloys was discussed. An amorphous alloy composition was found in thissystem and a melt-spinning amorphous alloy was produced in this composition. Through DSC analysis,the amorphous alloy exhibits high glass forming ability comparable to that of the InoueZr_(65)Al_(7.5)Cu_(17.5)Ni_(10) amorphous alloy.